Question

$4\, m ^{3}$ of water is to be pumped to a height of $20\, m$ and forced into a reservoir at a pressure of $2 \times 10^{5} \,N / m ^{2}$. The work done by the motor is (external pressure $=10^{5} \,N / m ^{2}$ )

• A. $ 8\times {{10}^{5}}J $
• B. $ 16\times {{10}^{5}}\,J $
• C. $ 12\times {{10}^{5}}\,J $
• D. $ 32\times {{10}^{5}}\,J $

Answer 1

Answer: (C)

Work done $W=m g h+\Delta p V $
$=V \rho g h+\Delta p V$
Here, $V=4 \,m^{3}, \rho=10^{3}\, kg / m ^{3}, g=10 \,m / s ^{2}$,
$h=20\, m, \Delta p=\left(2 \times 10^{5}-1 \times 10^{5}\right) \,N / m^{2} $
$\therefore W=4 \times 10^{3} \times 10 \times 20+\left(2 \times 10^{5}-1 \times 10^{5}\right) \times 4 $
$=8 \times 10^{5}+4 \times 10^{5} $
$=12 \times 10^{5} \,J$